A Markov model is a common statistical tool for modeling structured processes or phenomena that include randomness in both the output and the state of the process. Such models are used in many fields including in computational biology for modeling of protein family sequences, in speech recognition and in financial modeling. Markov models are generally represented by state diagrams showing both the emission probabilities and the transition probabilities of the system being modeled. Emission probabilities show the probabilities of certain outputs. Transition probabilities are the probabilities of changing the state of the model. State diagrams are useful for visualizing the architecture of the model and for seeing how the model can transition from one state to another. If the identity of the state itself is hidden from an outside observer, the Markov model is said to be a Hidden Markov model.
Unfortunately state diagrams do not represent an ideal method of conveying probability information from a Markov model to a user. Where there are a large number of states in the system being modeled, the state diagram may become confusing. Additionally, the state diagram may become too large to quickly provide information at a glance to a user as it may require several pages/display screens to display all of the states.
FIG. 1 depicts a state diagram 1 of a Hidden Markov model being used in profile alignment of amino acid sequences from a protein family. The circles represent states and the arrows represent state transitions. As the size of the state diagram grows, the transitions become more difficult to follow and represent in a concise manner to a user. For large models with a repetitive architecture, it is less important to see the representation of the architecture than it is to understand the changes in the emission and transition probabilities throughout the model.